Heat‐Driven Iontronic Nanotransistors

Abstract Thermoelectric polyelectrolytes are emerging as ideal material platform for self‐powered bio‐compatible electronic devices and sensors. However, despite the nanoscale nature of the ionic thermodiffusion processes underlying thermoelectric efficiency boost in polyelectrolytes, to date no evidence for direct probing of ionic diffusion on its relevant length and time scale has been reported. This gap is bridged by developing heat‐driven hybrid nanotransistors based on InAs nanowires embedded in thermally biased Na+‐functionalized (poly)ethyleneoxide, where the semiconducting nanostructure acts as a nanoscale probe sensitive to the local arrangement of the ionic species. The impact of ionic thermoelectric gating on the nanodevice electrical response is addressed, investigating the effect of device architecture, bias configuration and frequency of the heat stimulus, and inferring optimal conditions for the heat‐driven nanotransistor operation. Microscopic quantities of the polyelectrolyte such as the ionic diffusion coefficient are extracted from the analysis of hysteretic behaviors rising in the nanodevices. The reported experimental platform enables simultaneously the ionic thermodiffusion and nanoscale resolution, providing a framework for direct estimation of polyelectrolytes microscopic parameters. This may open new routes for heat‐driven nanoelectronic applications and boost the rational design of next‐generation polymer‐based thermoelectric materials.


S. I. Molecular Dynamics Simulations
Multi-scale simulations of the system are performed following the scheme illustrated in Fig S1. (a) We first define a monomer-based mapping of the atomistic structure to a CG one. Each monomer is described by a single bead for the group -CH2-O-CH2-(7 atoms) while the extremal one include only -CH2-OH (5 atoms) for the neutral end, or -CH2-O -(4 atoms) for the charged one. The Na + ion is represented atomistically. The CG bead is placed on the center of mass of the group. (b) Classical atomistic simulations are performed mixing randomly 500 9-mer PEG neutral chains with 500 dissociated PEO-Na chains (500 PEOand 500 Na + ). The simulation setup is reported in the panel. The general CHARMM FF was assigned (using CGenFF program) for PEO chains 1 , 2 . The partial charges were rescaled of a factor 0.8 with respect to the original partial charges of PEO following a common prescription for ionic liquids 3 , 4 . The partial charge of Na+ ions was extracted from a Car-Parrinello MD simulation of a pre-equilibrated system including of 8 PEO and 8 PEO -Na + in a cubic box of 21 Å 3 . Ab initio calculations were performed with the software CP2K 5 using a standard setup 6 with Perdew-Burke-Ernzerhof (PBE) exchange and correlation functional and Grimme's third-generation dispersion corrections (D3). The system was relaxed for 14 ps and the final conformation was used to evaluate the Restrained Electrostatic Potential (RESP) charges 7 . The classical atomistic trajectories are postprocessed by coarse graining according and subsequently the distributions of the internal coordinates (bead-bead distances, angles and dihedrals) are built as reference for the parameterization. (c) The Potentials of Mean Force (PMF) obtained by Boltzmann inversion of the internal variables distribution is then used to parameterize the CG-FF according to a protocol previously used for minimalist models of proteins 8 , 9 . The Force Field terms and parameterization finally used is reported in Table S.1. Simulations are performed with the setup reported in the panel and diffusion coefficients of the different components are evaluated. It is to be remarked here that the D reported in the plot accounts for the fictitious acceleration factor due to the coarse graining. This factor is extremely variable depending on the system. In this case it was evaluated to be ~300, by comparing the first relaxation phases of the atomistic systems to that of the CG system. The t* reported in the plot of the diffusion coefficient is renormalized by this factor. Accordingly renormalized D coefficient lie in the experimental range. Panel c also reports a representation of the system with the different components delimited by isosurfaces of the average densities in corresponding color, evaluated averaging over the last ~100 ns of simulation. The charged component (red and green) appear to form a percolated cluster separated by the neutral one (grey). The cluster formation is confirmed by the snapshots taken at the end of simulation, where chains of alternating Na+ with the polar head of the dissociated PEO are visible. Nevertheless, the ionic components appear to diffuse (see inset of D plot in (c), where the trajectories of a selected molecule for each component is reported). The diffusion mechanism of Na+ appears to occur by hopping along these chains, and therefore is more efficient than the one of the polymeric components. This is compatible with its ~1.4 factor larger mobility of Na+ with respect to the anionic polymeric component.

Bead types Composition Mass Charge Na
Na

FF Terms
Analytic form parameters  The diffusion mechanisms are better understood in the Supporting Movies (box.mpg and hop.mpg). In the first one we highlight one molecule per component with respect to the rest of the molecules in the box (shown as transparent). The larger mobility of Na + (in green) is apparent and also visible is the motion occurring by hopping. This is even clearer in the second movie (hop.mpg) where a single Na + ion is highlighted in yellow and observed to hop along the chains of alternating Na + (green) and polar head O -(red) of the dissociated PEO (static images from the movies are reported in Fig S.2 for reference to the movies given in separate files).

S.II.a: FTIR Spectra
After the synthesis of Na functionalized PEO samples as described in the experimental methods of the main text, samples were analyzed by means of Fourier Transform Infrared Spectroscopy in order to determine the success of the functionalization procedure. A typical acquisition is reported in Figure S3

S.II.b: Ion gating operation with Na-functionalized PEO
Prior to thermoelectric gating measurements, we perform conventional ion gating measurements by driving the polyelectrolyte with the application of a DC voltage to a metallic counter-electrode. The achieved field effect modulation of the electrical conductivity of the nanowire, reported in Figure S4, is compatible with the functionalization performed on the polymer and the presence of free ions able to perform ion gating.

S.II.c: Device operation with non-functionalized polymer
In order to assess the origin of the modulation of the electrical conductivity of the nanowire, device operation was tested when the nanowire is immersed in a droplet of non-functionalized droplet of polyethyleneoxide (molecular weight 400 g/mol). The droplet was treated as an electrolyte gate and a DC voltage bias was applied to a counter-electrode, in order to perform conventional field effect modulation of the electrical transport properties of the nanowire by means of ion gating, if any ion is present natively in the polymer. Figure S5 shows that absolutely no field effect modulation is achieved, clearly due to the absence of any ion in the nonfunctionalized electrolyte. This means that even if thermally driven, the non-functionalized droplet is not capable of performing field effect on the semiconducting nanowire. Moreover, we also fed the heating elements similarly to what is reported in the main text, finding out that due to the absence of the ions in the droplet no relevant modulation of I DS is achieved.

S.II.d: Device operation without polyelectrolyte
In order to exclude any spurious contribution on the modulation of the electrical conductivity of the nanowire not coming from the polyelectrolyte, we have tested device operation without applying any droplet on the device. We have injected the heating current through the metallic heaters and measured the current flowing in the nanowire, similarly to what is reported in the main text for thermoelectric gating experiments. In this case, if the heating of the substrate is such that an abrupt change in temperature in caused locally on the nanowire, its resistance may vary due to the dependence of the electrical resistance on temperature. As clearly visible in Figure S6, this is not the case, confirming that the observed modulation of the nanowire electrical conductivity is caused by the accumulation of sodium cations rather than any thermal effect unrelated to the employed polyelectrolyte. Figure S6: Current flowing through the nanowire when the heating element is fed, and no droplet is casted on the device. The temperature variation due to the substrate heating is not relevant for the modulation of the resistance of the nanowire.

S. III. Finite Element Modeling
The finite element analysis of the system has been performed with COMSOL Multiphysics suite. Local temperature at the heater location is computed by calculating the electric field and current density in the metallic serpentine, and used as heat source for the heat equation in the polyelectrolyte droplet: The model can be used to compute the spatial distribution of mass, charge, and temperature for specific operational configurations determined by heating current amplitude and frequency and waiting time between current application and system measurement, meaning that the simulation lets the system evolve in time for a time interval equal to the experimentally waited time between measurements. Figure S7: (a) Computed temperature profile for ℎ = 75 . (b) Temperature difference between the points located at ( 0 , 0 ) = (0 , 0 ) and ( 1 , 1 ) = (7 , 0 ) sweeping the heater feeding current as explained in the main text.